D. Maystre

Multipole method for microstructured optical fibers. I. Formulation

We describe a multipole method for calculating the modes of microstructured optical fibers. The method uses a multipole expansion centered on each hole to enforce boundary conditions accurately and matches expansions with different origins by use of addition theorems. We also validate the method and give representative results.

Multicoated gratings: a differential formalism applicable in the entire optical region

We present a new formalism for the diffraction of an electromagnetic plane wave by a multicoated grating. Its basic feature lies in the use of a coordinate system that maps all the interfaces onto parallel planes. Using Maxwell’s equations in this new system leads to a linear system of differential equations with constant coefficients whose solution is obtained through the calculation of the eigenvalues and eigenvectors of a matrix in each medium. Through classical criteria, our numerical results have been found generally to be accurate to within 1%. The serious numerical difficulties encountered by the previous differential formalism for highly conducting metallic gratings completely disappear, whatever the optical region. Furthermore, our computer code provides accurate results for metallic gratings covered by many modulated dielectric coatings or for highly modulated gratings. We give two kinds of applications. The first concerns the use of dielectric coatings on a modulated metallic substrate to minimize the absorption of energy. Conversely, the second describes the use of highly modulated metallic gratings to increase this absorption.

Scattering by a random set of parallel cylinders

A theory of scattering by a finite number of cylinders of arbitrary cross section is presented. This theory is based on a self-consistent approach that identifies incident and scattered fields around each cylinder and then uses the notion of a scattering matrix in order to get a linear system of equations. Special attention is paid to the simplified case of a sparse distribution of small cylinders for low frequencies. Surprisingly, it is found that the classical rules of homogenization must be modified in that case. The phenomenon of enhanced backscattering of light is investigated from numerical data for a dense distribution of cylinders.

The total absorption of light by a diffraction grating

Abstract This paper describes both theoretically and experimentally a phenomenon in which a gratinng with very shallow grooves absorbs virtually all of the light of a given wavelength which is incident upon it.

Grating efficiency theory as it applies to blazed and holographic gratings

Recently developed rigorous theories have been used to investigate the diffraction efficiency behavior of both blazed and holographic gratings. In order to assist designers of spectrometric systems we have covered a complete range of blaze angles for triangular grooves and modulations for sinusoidal groove shape in first and second orders. Several types of mountings are included together with the role played by finite conductivity of aluminum. Useful classifications of both types of gratings are given, as they apply from the near uv to ir regions. Comparisons showing the close agreement between theory and experiment are presented.

Rigorous theoretical study of finite-size two-dimensional photonic crystals doped by microcavities

We use a rigorous method for diffraction by a finite set of parallel cylinders to study the influence of defects in a photonic crystal. The method allows us to give an accurate description of all the characteristics of the electromagnetic field (near-field map, scattered field, and energy flow). The localized resonant modes can also be computed. We show some of their symmetry properties and the influence of coupling between two neighboring defects. Finally, an example is given, which shows that a slight local change in the crystal period can be used for the realization of devices that radiate energy in a very narrow angular range.

Scattering from metallic and dielectric rough surfaces

Using a generalization of the integral theory of metallic and dielectric gratings developed in our laboratory 15 years ago, we propose a rigorous integral theory of scattering by metallic or dielectric nonperiodic rough surfaces leading to a single integral equation. The numerical implementation has been carried out despite strong difficulties for TM polarization and metallic surfaces because of propagation of surface plasmon waves outside the illuminated region of the rough surface. Numerical results show the influence of the statistical parameters of the asperities on the absorption phenomena for metallic surfaces. Then the influence of asperities on the total transmission around Brewster incidence is studied. Finally numerical results of enhanced backscattering from perfectly conducting, metallic, and dielectric random rough surfaces are given.

A new general integral theory for dielectric coated gratings

We present a new rigorous integral formalism for the theoretical study of dielectric coated gratings and grating couplers. It applies in the resonance domain, where the wavelength of the incident field and the groove spacing are of the same order of magnitude. The computed program issued from this theory extends the domain of application of the previous differential or integral theories. It can be used to investigate, with a very good accuracy, the properties of bare or dielectric coated gratings, for any groove shape and any polarization, in the entire visible, ultraviolet, and infrared regions. Various classical criteria are used to control the validity of the numerical results and comparisons are made with the numerical results obtained using the previous integral and differential formalisms. Two examples of applications are given. First, we show that the new possibilities of our program lead to a better agreement between theoretical results and experimental data. Second, a theoretical study of a certain type of grating coupler is given.

On the theory and solar application of inductive grids

A brief description is given of the rigorous formulism of Chen, which describes the diffraction by perfectly-conducting inductive grids. The formulism is used to prove several general properties of grids, including the relevant form of the Reciprocity Theorem. The theory is used to investigate the equivalent circuit model proposed by other authors for thin grids, and also to derive a monomodal model of the type first proposed by Chen. The latter model is shown to be useful even in the region where more than one spectral order propagates.The accuracy of the formulism is established by the comparison of calculated results with a number of far-infrared measurements on grids. The use of grids as solar-selective elements is investigated. They are shown to be capable of providinga/e ratios of the order of 30–40, provided that they are always pointed towards the sun, and that the diffuse content of the illumination is low.

Electromagnetic study of photonic band gaps

Using a rigorous integral theory of diffraction gratings, we investigate the properties of two-dimensional photonic crystals made with lossless dielectric materials using a model where the crystal is represented by a finite stack of dielectric grids of infinite extension. After studying the influence of the thickness of the crystal, we analyse the variations of the properties of the gap with the filling ratio, the index of dielectric, the geometry of the crystal, the shape of the rods, the polarization and finally with a contrast inversion. The validity of this multi-grid model is checked by varying the angle of incidence, which appears to have a significant influence. Some surprising properties emerge from these results, in particular the fact that contrast inversion has opposite effects according to whether the incident wave is s or p polarized. Finally, we give a very simple empirical rule that enables one to predict with a good precision the location of the centres of the gaps.